Labour's policy, "whatever it turns out to be" is an irrelevance now, because most of their potential voters are choosing to vote for clearly defined Leave or Remain parties. Arguably a vote for the Lib Dems, 6% ahead of Labour in latest YouGov poll is a more definitive vote for Remain than a vote for a Labour party which no one quite knows where it will end up.

By your own logic, a vote for the Lib Dems is the way to do as much damage as possible to the Brexit Party right now. See also the trend...

I still fail to see how a vote at the European election influences anything with the possible exception of a BREXIT blowout. Will Theresa May feel morally obliged to run a second referendum? Boris Johnson? Nearly all of Labour already voted for a second referendum. There were something like 40 defections? How many of those would switch the vote even if Corbyn whipped until his hands fell off?

That is why I focus on the trend of all polls, although even that didn't help me much with the last US Presidential election.

Personally I think the outcome is very hard to predict because turnout is hard to predict. Will Remainers treat it as a proxy referendum on membership and so turn out in force? Are hard core Brexiteers the most angry and motivated to turn out? We know many Tories won't bother to vote, but what about most Labour supporters?

As for impact/influence, a runaway victory for the Brexit party would provide BoJo with the mandate he needs for a no deal Brexit. Conversely, if the combined Remainer parties out poll the combined Leaver parties, that would increase pressure for a formal second referendum.

The final result is no more binding on the political parties than the Brexit referendum was, but we saw how much political influence that has had. Either way, I think May's deal is dead, especially if the Brexit party out polls the Tories and Labour combined - a distinct possibility.

It will be no deal or no Brexit, and that could be determined by how well the Remainer parties do.

No, that's not going to happen. British politics is Winner Takes All and there is zero point pretending there's a vague aspirational coalition of Remain intention when no such coalition exists, formally or otherwise.

The British media certainly aren't go to read it like that.

It is absolutely guaranteed that if - when? - Farage wins by a big majority over the runner-up party, he will claim a mandate for No Deal.

And the Tory media and some of the supposedly not-so-Tory media will echo that.

The only way to prevent that would have been to allow Labour to beat TBR. But the LDs have run a very effective spoiler campaign, so that's not going to happen now.

They're clearly happy with second place, and second place is the best they'll get - which may appear to be good news for them, but it's going to be an utter PR disaster for Remain.

Voters literally do not understand PR in the UK. There is no public concept of power-sharing or consensus negotiation.

It's all about winners and losers - which is why we have the (now majority) Remain voters being ignored, while Leavers bang on about how they won a referendum and Westminster has to do everything they want.

But that is the point: The non-binding referendum only became The Will of The People™ because May offered a vision forward for the Tories after Cameron dropped the ball: Use Brexit to absorb the far-right back into the party and wipe out Labour in a moment of weakness. Everything else followed from there.
So the question of mandates doesn't really arise. The question is what can they get away with?

I think there is also a second side to this: Usually you'd expect the centrist media to switch immediately from this referendum is of the utmost importance, read all about it in these pages, to well it was advisory and doesn't mean much. Sure, the right wing money boys want to see the country burn and loot the corpse, but the ruling class faction broadly collected behind the Blairites want buisness as usual. So why did they sit on their hands here? The main story they were pushing at the time was that Corbyn lost the referendum and had to go. Can't simultaneously argue that it didn't mean anything.